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On the construction of a new generalization of Runge–Kutta methods

✍ Scribed by Mark Sofroniou; Giulia Spaletta

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
409 KB
Volume
74
Category
Article
ISSN
1571-0661

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✦ Synopsis

We give an overview of the construction of algebraic conditions for determining the order of Runge-Kutta methods and describe a novel extension for numerically solving systems of differential equations. The new schemes, called Elementary Differential Runge-Kutta methods, include as a subset Runge-Kutta methods, Taylor series methods, Multiderivative Runge-Kutta methods. We outline how order conditions have been constructed for the new schemes using B-series and their composition and give details relating to a Mathematica implementation.

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